An introduction to $V$-filtrations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910327003676672 |
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| author | Chen, Qianyu Dirks, Bradley Mustaţă, Mircea |
| author_facet | Chen, Qianyu Dirks, Bradley Mustaţă, Mircea |
| contents | We give an introduction to the theory of $V$-filtrations of Malgrange and Kashiwara. After discussing the basic properties of this construction (in the case of a smooth hypersurface and, later, in the general case), we describe the connection with the theory of $b$-functions. As an example, we treat the case of weighted homogeneous isolated singularities. We discuss the compatibility of $V$-filtrations with proper push-forward and duality and the connection with nearby and vanishing cycles via the Riemann-Hilbert correspondence. We end by describing some invariants of singularities via the $V$-filtration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An introduction to $V$-filtrations Chen, Qianyu Dirks, Bradley Mustaţă, Mircea Algebraic Geometry 14F10, 32S40, 14B05 We give an introduction to the theory of $V$-filtrations of Malgrange and Kashiwara. After discussing the basic properties of this construction (in the case of a smooth hypersurface and, later, in the general case), we describe the connection with the theory of $b$-functions. As an example, we treat the case of weighted homogeneous isolated singularities. We discuss the compatibility of $V$-filtrations with proper push-forward and duality and the connection with nearby and vanishing cycles via the Riemann-Hilbert correspondence. We end by describing some invariants of singularities via the $V$-filtration. |
| title | An introduction to $V$-filtrations |
| topic | Algebraic Geometry 14F10, 32S40, 14B05 |
| url | https://arxiv.org/abs/2402.07816 |